Malcolm Turnbull has denounced the "witch-hunt" underway in Australian politics. Photo: AAP

Prime Minister Malcolm Turnbull has slammed the door shut on a citizenship audit of all federal MPs, but Labor has responded by calling for the major parties to work together and end the citizenship crisis.

A fired-up Mr Turnbull arrived back in Australia on Friday and angrily hit back at calls for an audit of all parliamentarians' citizenship status, declaring "we have no place in Australia for witch-hunts" and slamming a report that suggested Energy and Environment Minister Josh Frydenberg could be a dual Hungarian-Australian citizen.

While defending Josh Frydenberg over dual citizenship claims, a fired up Malcolm Turnbull says his mother was rendered stateless by Germans and fascists who treated Jews as subhuman and it's a miracle she wasn't killed in the Holocaust.

But in a move that potentially wedges the government, Opposition Leader Bill Shorten extended an olive branch to the Prime Minister, proposing "a process such as universal disclosure to the Parliament" that, although short on detail, could offer a way through the impasse.

Fairfax Media spoke to seven members of Mr Turnbull's cabinet on Friday, and confirmed the subject of a citizenship audit was set to be discussed when cabinet next meets in Canberra on Monday night – though it is unlikely at this stage that public pressure will shift the government's position.

Those cabinet ministers – who asked not to be named so they could freely discuss their views on the matter – argued against an audit because requiring an MP to prove they were not a dual citizen, which is forbidden by section 44 of the Constitution, would reverse the onus of proof.

All conceded public trust in Parliament had been eroded by the citizenship fiasco, but just one said a compromise solution – such as a parliamentary committee examining the issue, rather than an external audit – could be the way forward.

The Prime Minister said any member of Parliament could refer a colleague to the High Court to have their citizenship credentials examined, and said the court was the only institution with the authority to deal with dual citizenship issues.

He said "witch-hunts" – a term also used by Treasurer Scott Morrison and Attorney-General George Brandis – were "not our way".

"Has this witch-hunt become so absurd that people are seriously claiming that Josh Frydenberg is the citizen of a country which has stripped his mother and her family of their citizenship and would have pushed them into the gas chambers had it not been that the ... war was ended before they had time to do so?" the Prime Minister said.

"The Parliament has the power to refer any member or Senator to the High Court on this question of eligibility and the High Court alone has the ability to determine it."

Mr Shorten's acknowledgement that "more needs to be done to restore faith confidence in the system" came a day after Fairfax Media revealed Labor was preparing to shift position.

It would see the ALP release the paperwork of its MPs whose citizenship was in question, which it has thus far refused to do.

"Whatever the ultimate process is, it must adhere to clear principles. It must be accountable to the people through the Parliament. It must have bipartisan agreement prior to implementation. It must be sufficiently robust to give all Australians confidence in the process," Mr Shorten said.

"But it must not be allowed to create more legal problems, or in any way undermine the supremacy of the High Court on these matters."

Mr Turnbull bristled at the report there was a "50 per cent likelihood" that Mr Frydenberg could hold Hungarian citizenship via his mother, and pointed out Mrs Frydenberg had fled Hungary at the end of the war and, "it is is a miracle they weren't killed, as so many of their relatives were".

"Three quarters of all the Jews in Hungary were murdered in the Holocaust," Mr Turnbull said. "They were rendered sub-human in the eyes of the fascists and the Nazis. I wish that ... those who make these allegations about Josh Frydenberg could think a little deeper about the history of the Holocaust."

Mr Frydenberg said the idea he was a dual citizen was "absurd", and said that a formal application process was required to become a Hungarian citizen.

"It's absurd to think you could become a citizen of a country unwillingly," he said.

Mr Frydenberg's mother lived in a displaced persons' camp and gained entry to Australia in 1950 as a "stateless" person. She became an Australian citizen in 1957.

The Prime Minster side-stepped questions about the revelation that Communications Minister Mitch Fifield knew for weeks that former Senate president Stephen Parry could be a dual citizen of the UK, but said nothing.

Mr Turnbull only found out on Tuesday that Mr Parry was set to quit because of his dual nationality.

Mr Shorten accused Senator Fifield and Mr Parry of an "incredibly alarming" cover up of the former Senate president's status, and said the government had "no plan to resolve the citizenship crisis".

The High Court's ruling on dual citizenship has cost the Turnbull government former deputy prime minister Barnaby Joyce and former cabinet minister Fiona Nash, while Mr Parry sensationally revealed he was a dual UK citizen and quit, too, earlier this week.

The deepening crisis has already prompted calls from the Coalition and Labor backbench for an audit of all MPs; this idea has also been advocated by Greens leader Richard Di Natale, and crossbench senators Cory Bernardi and Derryn Hinch.